The invention concerns a magnet arrangement for generating a magnetic field in the direction of a z-axis in a working volume disposed on the z-axis about z=0, with a magnet coil system which comprises one or more superconducting magnet partial coil systems, each forming superconductingly short-circuited current paths in the operating state, and with a further coil system which can be charged or discharged independently of the magnet coil system and comprises a first and a second partial coil system, wherein the first partial coil system and the second partial coil system each comprise at least one coil, wherein all coils of the further coil system are connected in series, wherein gCeff,diamag>0.1 mT/A.
The above-mentioned variable is defined as follows:gCeff,diamag=gC−gAT·(LAdiamag)−1·LC→Adiamag+gM with:gC: field per ampere current of the further coil system in the working volume without the field contributions of the magnet partial coil systems and without the field contribution of the magnetization of superconductor material in the magnet arrangement.gAT=(gA1, . . . , gAj, . . . gAn),gAj: field per ampere current of the j-th magnet partial coil system in the working volume without the field contributions of the i-th magnet partial coil systems for i≠j and without the field contributions of the further coil system and the magnetization of superconductor material in the magnet arrangement,LAdiamag: n×n inductance matrix of the magnet partial coil systems in case of complete diamagnetic expulsion of field changes from the superconducting material volume in the magnet arrangement.
      L          C      →      A        diamag    =      (                                        L                          C              →                              A                ⁢                                                                  ⁢                1                                      diamag                                                ⋮                                                  L                          C              →              An                        diamag                                )  LC→Aidiamag: mutual inductance of the further coil system with the i-th magnet partial coil system in case of complete diamagnetic expulsion of field changes from the superconducting material volume in the magnet arrangement,gM: field in the working volume which is due to the magnetization of superconductor material in the magnet arrangement with a current change of one ampere in the further coil system in case of complete diamagnetic expulsion of field changes from the superconducting material volume in the magnet arrangement and taking into consideration the induced currents in the magnet partial coil systems.
A magnet arrangement of this type is already disclosed in [1].
In superconducting magnet arrangement applications, e.g. in the field of electron spin resonance (EPR/ESR), the magnetic field must preferably be linearly changed with time (“sweeping”). This is also called a field ramp.
In order to obtain a high resolution with such a sweep process, a further coil system (also called field coil or “sweep coil”) must be used in addition to the superconducting magnet coil system, which produces a strong background field [1]. Sweeping with a further coil system instead of the superconducting magnet coil system itself is advantageous, in particular, since the heat input into the superconducting magnet coil system can be reduced because of the smaller currents that are used during sweeping with the further coil system [2]. The further coil system may thereby be normally conducting (e.g. a copper coil cooled with water) or be superconducting.
One example of a superconducting further coil system is provided in the commercial magnet system “cryogen-free superconducting ESR 12 T magnet system” by Cryogenic [3].
[4] describes a magnet arrangement with an additional current-carrying coil system with
                    g        C                  eff          ,          class                            g        C                  eff          ,          diamag                      >    1.2    ,whereingCeff,class=gC−gAT·(LAclass)−1·LC→Aclass,LAclass: n×n inductance matrix of the magnet partial coil systems, thereby neglecting any diamagnetic expulsion of fields from the superconducting material in the magnet arrangement,
            L              C        →        A            class        =          (                                                  L                              C                →                                  A                  ⁢                                                                          ⁢                  1                                            class                                                            ⋮                                                              L                              C                →                An                            class                                          )        ,LC→Aiclass: inductance of the further coil system with the i-th magnet partial coil system, thereby neglecting any diamagnetic expulsion of fields from the superconducting material in the magnet arrangement.
Non-linear effects with respect to the field strength can occur in case of current changes in superconducting magnets [5]. This is generally called hysteresis. This means that the magnet produces a field which depends on the history of the current in the magnet [3, 6, 7]. The mechanism in a magnet arrangement with a superconducting magnet coil system, which produces a hysteresis during a field ramp with a further coil system, is as follows: During charging of the further coil system, a field is normally also generated in the volume of the superconducting magnet coil system. This field change is initially expelled by the superconductor material, whereby the effective field strength per ampere of the further coil system gCeff,diamag can be increased or weakened compared to the value gCeff,class which would be obtained without field expulsion by the superconductor material. The field expulsion of the superconductor material in case of field changes due to charging of the further coil system decreases above a certain field changing amplitude. In this regime, the field strength of the further coil system per ampere current change varies from gCeff,diamag to gCeff,class. When the charging direction of the further coil system is changed, the field strength per ampere current change is initially again gCeff,diamag. The dependence of the field strength of the further coil system on the current is thus non-linear, with hysteresis.
Inductive coupling of the further coil system to the magnet coil system may moreover also be problematic and is sometimes interpreted as the source of the hysteresis [1].
Magnetic field changes also generate eddy currents (e.g. in the coil bodies). The problem is known from MRI (in particular with gradient coils). The field changes during sweeping of e.g. EPR systems are normally slower (typically from 1 G/s to 50 G/s [1]) than the field changes of the gradient coils in MRI, and the eddy currents are therefore weaker. The expected result is nevertheless a time delay of the field in the magnet center [8].
Literature describes the following methods in order to perform measurements during a sweep, despite hysteresis:
In the method presented in [6], the magnetic field is measured during a sweep (e.g. with a Hall probe) and the current is directly adjusted. One problem thereby is that the field is not exactly measured at the position of the sample. During sweeping, the field measurement is influenced by the inhomogeneity of the field of the further coil system.
The magnet is often calibrated (measurement of the magnetic field in dependence on the current B(I) with a known sample) [1, 6, 7]. The hysteresis depends, however, on the sweep amplitude and on the sweep rate [5]. This method is therefore only practical when only one sweep amplitude and one sweep rate are used.
Another alternative is to operate the magnet arrangement in the “driven mode”. The magnet coil system is thereby not made persistent with a switch, but the field is kept constant by the power supply unit [3]. This method requires an additional power supply unit which must be very stable. Moreover, a high cooling liquid loss must be accepted due to the current that must constantly flow in the feed line.
One possibility for reducing the hysteresis is the use of a field coil that generates very small field strengths. In this case, the field-current curve of the further coil system shows the initial slope gCeff,diamag over the entire sweep range and never enters the “classical” regime.
Field coils with a small “sweep” range are disclosed in AC applications under the name modulation coils. Such modulation coils change the field with high frequency (kilohertz range) in a harmonic fashion but only within a small range. The coverage of a large sweep range is not possible with such modulation coils.
In contrast thereto, it is the object of the present invention to propose a magnet arrangement, wherein the field change in the working volume is preferably a linear function of the current change in the further coil system which can be charged or discharged independently of the magnet coil system.